Some situation at a college where they'll give you a cookie if you take an STD test seems quite likely

You situation does not really count as no cost though. In a world in which you must spend effort to avoid getting a STD test it seems unlikely that plausible deniability can be generated in the first place.

I don't see how the situation is meaningfully different from no cost. "I couldn't be bothered to get it done" is hardly an acceptable excuse on the face of it, but despite that people will judge you more harshly when you harm knowingly rather than when you harm through avoidable ignorance, even though that ignorance is your own fault. I don't think they do so because they perceive a justifying cost.

I think the point that others have been trying to make is that gaining the evidence isn't merely of lower importance to the agent than some other pursuits, it's that gaining the evidence appears to be actually harmful to what the agent wants.